BRIEF NOTEJapanese Journal of Applied Physics 59, 058002 (2020)
https://doi.org/10.35848/1347-4065/ab8023

Strain and temperature dependencies of multimodal interference spectra inhetero-core-fiber structures
Yosuke Mizuno1,2* , Sonoko Hagiwara2, Heeyoung Lee3 , Neisei Hayashi2 , Michiko Nishiyama4,
Kazuhiro Wanatabe4, and Kentaro Nakamura2
1

Faculty of Engineering, Yokohama National University, Yokohama 240-8501, Japan
Institute of Innovative Research, Tokyo Institute of Technology, Yokohama 226-8503, Japan
3
College of Engineering, Shibaura Institute of Technology, Tokyo 135-8548, Japan
4
Faculty of Science and Engineering, Soka University, Tokyo 192-8577, Japan2*

E-mail: mizuno-yosuke-rg@ynu.ac.jp

Received February 8, 2020; revised March 5, 2020; accepted March 16, 2020; published online April 16, 2020
We investigate, for the first time, the temperature and strain dependencies of the spectral dips of the multimodal interference patterns in heterocore-fiber structures at telecom wavelength. With increasing temperature and strain, the spectral dips shifted to shorter wavelengths withdependence coefficients of –3.5 nm °C−1 and –0.62 pm/με, respectively. Their absolute values were ∼60 times larger and ∼30 times smaller than
the temperature and strain sensitivities of a standard single-mode-multimode-single-mode sensor, respectively. This result implies that the heterocore-fiber structures can be potentially used to develop highly sensitive temperature sensors with reduced strain sensitivity.
© 2020 The Japan Society of Applied Physics

Among a variety of optical ﬁber sensors that have beendeveloped so far for structural health monitoring,1–6) we
focus on what we call a hetero-core ﬁber structure, in which asmall-core single-mode ﬁber (SMF) is sandwiched (spliced)
between two normal-core SMFs.7–11) By exploiting theoptical loss caused by bending, the hetero-core structure
has been used as a power-based bending-angle sensor. It has
a lot of advantages, such as insusceptibility to temperature,7)high-speed operation,8) and controllability of sensitivity by
the core diameter, etc.9) and has been used to develop
numerous commercially available devices. The hetero-coreﬁber sensors will be more useful in practical applications, if
temperature or strain can be measured in addition to bending
angle while the sensor structure is maintained.
One method for achieving this aim is to exploit themultimodal interference in the hetero-core-ﬁber structure—aphenomenon in which multiple propagating lights withdifferent modes in multimode ﬁbers (MMFs) interfere with
one another.12) Consequently, the spectrum of the transmitted
light exhibits characteristic peaks and dips, which shift bytemperature change or applied strain. Therefore, by measuring the shift of one (or some) of the peaks/dips, temperature and strain can be estimated. One of the simplest
conﬁgurations for implementing modal-interference-based
sensors is a so-called single-mode-multimode-single-mode(SMS) structure.13–20) This is in analogy with the heterocore-ﬁber structure, in which multiple propagation modes
exist in the cladding layer of the small-core SMF in addition
to the core mode. Although the multimodal interference inthe hetero-core-ﬁber structures has been already observed21)
and its dependencies on refractive index and humidity havebeen clariﬁed,22,23) its strain and temperature sensing characteristics remain to be unclariﬁed.
In this work, we investigate the temperature and strain
dependencies of the interference spectra in the hetero-coreﬁber structures. We ﬁnd that, at ∼1580 nm, with increasing
temperature and strain, a characteristic dip shifts to shorter
wavelengths with dependence coefﬁcients of –3.5 nm °C−1
and –0.62 pm/με, respectively. These values indicate that,compared to conventional silica-ﬁber-based SMS sensors,
hetero-core-ﬁber-based SMS sensors may enable highly

sensitive temperature measurement with small strain sensitivity.
The operating principle of SMS-based temperature andstrain sensing is simple. When light is injected from the ﬁrst
SMF into an MMF (sensing head), multiple modes are
excited and travel along the MMF with their own propagation
constants. At the other end of the MMF, the net ﬁeld coupled
to the second SMF is determined by the relative phasedifferences among all the propagation modes. Under theassumption that the MMF and the two SMFs are perfectly
axially aligned, the optical output power from the second
SMF, Pout, can be given as18)
Pout = ∣ a 0 2 + a1 2 exp i (b 0 - b1) L+ a 2 2 exp i (b 0 - b 2 ) L + ∣2 ,(1 )where aj is the ﬁeld amplitudes of the jth modes at the ﬁrst
SMF-to-MMF boundary, βj is the propagation constants of
the jth modes, and L is the length of the MMF. It is clear that
Pout is inﬂuenced by temperature change and strain applied to
the MMF (with some change in βj and L). Thus, temperatureand strain sensing can be performed by measuring the shift ofthe spectral dips (or peaks) of the modal interference pattern.
Considering that multiple propagation modes exist in thesmall-core ﬁber of the hetero-core-ﬁber structure, temperature and strain sensing should be feasible in the same manner.
The experimental setup is depicted in Fig. 1. We used thehetero-core-ﬁber structures involving small-core SMFs (corediameter: 3 μm, loss: 50 dB m−1 at 488 nm) spliced withnormal-core SMFs (core diameter: 9 μm, loss: 0.25 dB km−1
at 1550 nm). The lengths of the small-core SMFs were
210 mm and 180 mm for temperature and strain characterizations, respectively. The lengths of all the normal-core SMFs
were ∼2 m. The 100 mW output of a supercontinuum source(SCS; bandwidth: 460–2000 nm) was injected in the heterocore-ﬁber structure, and the spectrum of the transmitted light
was observed using an optical spectrum analyzer (OSA).
Temperature change and strain were applied to the whole
length of the MMF using a thermostatic chamber andtranslation stages, respectively. The room temperature was
28 °C.

058002-1© 2020 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 59, 058002 (2020)

Y. Mizuno et al.

Fig. 1. (Color online) Experimental setup for observing multimodal
interference caused in hetero-core-ﬁber structure. OSA: optical spectrum
analyzer, SCS: supercontinuum source, SMF: single-mode ﬁber.

power is not distributed to cladding modes in the small-core
SMF and that modal interference is less striking. The
magniﬁed view around 1590 nm is shown in Fig. 2(b).
Multiple clear dips were observed in this range, and weselected the dip around 1600 nm in the following temperature
characterization.
Then, we measured the temperature dependence of this

(a)

(b)

Fig. 2. (Color online) (a) Optical spectra measured before and after transmission through the hetero-core-ﬁber structure. (b) Its magniﬁed view around
1590 nm. The spectral dip in the red circle was used in the temperature characterization.

(a)

(b)

Fig. 3. (Color online) (a) Temperature dependence of the spectral dip (normalized). (b) Dip wavelength plotted as a function of temperature. The solid line isa linear ﬁt.

(a)

(b)

Fig. 4. (Color online) (a) Strain dependence of the spectral dip. (b) Dip wavelength plotted as a function of strain. The solid line is a linear ﬁt.

We ﬁrst measured and compared the optical spectra before
and after transmission through the hetero-core-ﬁber structure(involving a 210-mm-long small-core MMF), which correspond to the SCS output and the OSA input, respectively[Fig. 2(a)]. The optical power was reduced at all the
wavelengths, and the amount of the power loss was muchhigher at longer wavelengths. This is natural considering the
wavelength dependence of the propagation loss in the smallcore SMF. The spectrum after transmission exhibited multiple characteristic dips that were not observed in the SCS
output, especially at longer wavelengths. This is also naturalconsidering that, at shorter wavelengths, most of the optical

spectral dip as shown in Fig. 3(a). The vertical axis was
normalized so that the dip power became 0. With increasing
temperature, the spectral dip shifted to shorter wavelengths.
The dip wavelength dependence on temperature shown in
Fig. 3(b) was almost linear with a coefﬁcient of–3.5 nm °C−1. The linear coefﬁcient of determination (r2,the square of the correlation coefﬁcient) was as high as 0.999.
We also measured the strain dependence of the spectral dip
around 1579 nm (note that one of the clear dips was observedat this wavelength when another sample was used) as shownin Fig. 4(a). As strain increased, the dip also shifted to shorter
wavelengths. The dip wavelength dependence on strain

058002-2© 2020 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 59, 058002 (2020)

Y. Mizuno et al.

[Fig. 4(b)] shows that the strain coefﬁcient was –0.62 pm/με;
the r2 value was 0.998.
Subsequently, in addition to the measurement around1579 nm, we measured the strain dependencies of the spectra
and the dip wavelengths around 1486, 1517, and 1549 nm[Figs. 5(a)–5(f)]. The calculated strain coefﬁcients (the r2
values were all higher than 0.95) were then plotted as afunction of the dip wavelength at zero strain (Fig. 6). It isclear that the strain sensitivity does not largely depend on the
wavelength in this range.
Finally, to consider the sensing performance, let uscompare the absolute values of the obtained sensitivities
with those of a standard silica-based SMS sensor.13) The
obtained temperature coefﬁcient (3.5 nm °C−1) is approximately 60 times larger than the previously reported value(59 pm °C−1), whereas the obtained strain coefﬁcient(0.62 pm/με) is approximately 30 times smaller than that
previously reported (19 pm/με). Note that, although thepreviously reported values were obtained at different MMF
lengths and wavelengths, these two factors have beenreported not to have clear inﬂuence on thesensitivities.17,19) This result indicates a potential of highly
sensitive temperature sensing with reduced strain sensitivity.
In conclusion, we investigated the temperature and strain
dependencies of the spectral dips of the multimodal interference patterns in the hetero-core-ﬁber structures. At∼1580 nm, as temperature change and strain increased, theFig. 6. (Color online) Strain sensitivity plotted as a function of the dip
wavelength at zero strain.

spectral dips shifted to shorter wavelengths with dependence
coefﬁcients of –3.5 nm °C−1 and –0.62 pm/με, respectively.
Their absolute values were ∼60 times larger and ∼30 times
smaller than the temperature and strain sensitivities of astandard SMS sensor previously reported, respectively; thisresult indicates that the multimodal interference in the heterocore-ﬁber structures may be used to develop highly sensitive
temperature sensors with small strain sensitivity. Consideringthat the hetero-core-ﬁber sensors have been used to measurebending angle based on power information, this result thattemperature can be measured with high sensitivity based on
frequency information indicates that this structure could be
exploited for simultaneous sensing of temperature and

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 5. (Color online) Strain dependencies of the spectral dips around (a) 1486 nm, (b) 1517 nm, and (c) 1549 nm. Dip wavelength dependencies on strainaround (d) 1486 nm, (e) 1517 nm, and (f) 1549 nm. The solid lines are linear ﬁts.

058002-3© 2020 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 59, 058002 (2020)

Y. Mizuno et al.

bending angle. Combined use of multimodal interference andFabry–Perot interference will be another interesting topic to
be discussed in future.
Acknowledgments This work was supported by JSPS KAKENHI Grant
Numbers 17H04930 and 17J07226.
ORCID iDs Yosuke Mizuno
https://orcid.org/0000-0002-33624720 Heeyoung Lee
https://orcid.org/0000-0003-31790386 Neisei Hayashi
https://orcid.org/0000-0002-8956566X Kentaro Nakamura
https://orcid.org/0000-0003-2899-4484

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